Time: 20 minutes. This quiz is open book, open notes.
1. A batch A has the summary statistics listed below. The values in batch B are obtained by doubling each value in A and adding that to 10000. (For example, if 7 is in A, then 10014 is in B.) Compute the corresponding summary statistics for B. In cases where it is not possible to deduce the value, write "indeterminate,", or if the value is not defined, then write "not defined."
| Statistic | A | B |
| Count | 77 | |
| Median | -3.2 | |
| H-spread | 1.9 | |
| 95th percentile | -0.8 | |
| Variance | 11.0 | |
| Third order statistic (X[3]) | -12.3 | |
| Geometric mean | not defined | |
| 10% Trimmed mean | -3.5 |
Would you expect A to be positively skewed, negatively skewed, or have approximately zero skewness? What about B? Support your conclusions. Extra credit: Show how each one of the statistics above (apart from the count and geometric mean) provides evidence in support of your answer.
2. Draw a histogram of the following batch of bis (2-ethyl hexyl) phthalate measurements in groundwater (micrograms per liter). Choose bins in a way that helps portray the "shape" of the data.
0.24, 0.58, 0.77, 1.30, 3.23, 3.91, 7.71, 11.57, 13.51, 19.75, 24.57, 26.64, 37.85, 55.00, 60.05, 89.76
(The values have been sorted for you.) Label the histogram appropriately so that it can be read on its own. Use relative frequency on the y-axis.
3. A batch has 29 values. The five largest values are 33.0, 24.6, 17.0, 16.0, and 15.3 Compute the 95th percentile of this batch. Use Weibull plotting positions (the percentile at rank I is I/(N+1): text, page 96). Round the answer to one decimal place precision (the same as the data).
Scoring: The passing score is 95.
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